OK I know that! But......why do we have to be careful if we smoke not to go near people who are on oxygen? If you starve a fire of oxygen the fire will go out, won't it? Doesn't oxygen help a fire to burn? Please explain it! I'm at a loss!

Material cannot burn without oxygen. Oxygen itself will not burn, but oxygen assists burning. So, an oxygen enriched atmosphere will cause things that may already be near their flash point to burn and will cause thing taht are burning to accelerate and burn much more quickly.

If you light a cigarette in an oxygen enriched atmosphere, it will burn like a flare. But it is the tobacco and paper burning faster because of the presense of extra oxygen, not the oxygen itself burning.